CBSE Questions for Class 12 Commerce Applied Mathematics Linear Equations Quiz 4 - MCQExams.com

Find two numbers whose sum is $$15$$ and difference is $$3$$.
  • $$13$$ and $$2$$
  • $$7$$ and $$8$$
  • $$9$$ and $$6$$
  • $$3$$ and $$12$$
Solve the following pair of simultaneous equations:
$$\displaystyle \frac{a}{4}\, -\, \frac{b}{3}\, =\, 0\,;\, \frac{3a\, +\, 8}{5}\, =\, \frac{2b\, -\, 1}{2}$$
  • $$a = -4.5, b = 12$$
  • $$a = 4, b = -5$$
  • $$a = 14, b = 10.5$$
  • $$a = 12, b = 11.5$$
Solve the following pair of equations :
$$x-y= 0.9$$ and $$\displaystyle \frac{11}{2\left ( x+y \right )}= 1$$
  • $$x= 1.5;y= 4$$
  • $$x= 3;y= 2.5$$
  • $$x= 5.2;y= 0.3$$
  • $$x= 3.2;y= 2.3$$
Find a fraction which reduces to $$\displaystyle \frac{2}{3}$$ if the numerator and the denominator are each increased by $$1$$, and reduces to $$\displaystyle \frac{3}{5}$$ if the numerator and the denominator are each decreased by $$2$$.
  • $$\displaystyle \frac{13}{12}$$
  • $$\displaystyle \frac{11}{17}$$
  • $$\displaystyle \frac{9}{4}$$
  • $$\displaystyle \frac{13}{3}$$
Find two numbers, which differ by $$7$$, such that twice the greater added to five times the smaller gives $$42$$.
  • $$19$$ and $$12$$
  • $$12$$ and $$5$$
  • $$11$$ and $$4$$
  • $$16$$ and $$9$$
$$A$$ is $$25$$ years older than $$B$$. In $$15$$ years, $$A$$ will be twice of $$B$$. Find the present ages of $$A$$ and $$B$$.
  • Present age of $$A$$ is $$40$$ years and

    Present age of $$B$$ is $$15$$ years
  • Present age of $$A$$ is $$37$$ years and

    Present age of B is $$12$$ years
  • Present age of $$A$$ is $$35$$ years and

    Present age of $$B$$ is $$10$$ years
  • Present age of $$A$$ is $$45$$ years and

    Present age of $$B$$ is $$20$$ years
A man is 24 years older than his son. 12 years ago, he was five times as old as his son. Find the present ages of both.
  • Present age of father is $$44$$ years and Present age of son is $$20$$ years
  • Present age of father is $$42$$ years and Present age of son is $$18$$ years
  • Present age of father is $$60$$ years and Present age of son is $$36$$ years
  • Present age of father is $$48$$ years and Present age of son is $$24$$ years
Find the fraction such that it becomes $$\displaystyle \frac{1}{2}$$ if 1 is added to the numerator, and $$\displaystyle \frac{1}{3}$$ if 1 is added to the denominator.
  • $$\dfrac{3}{8}$$
  • $$\dfrac{1}{6}$$
  • $$\dfrac{8}{7}$$
  • $$\dfrac{7}{3}$$
Solve the following pair of linear (simultaneous) equations by the method of elimination:
$$2x+3y= 8$$
$$2x= 2+3y$$
  • $$x= 3$$ and $$y=6$$
  • $$x= 5.5$$ and $$y=-4$$
  • $$x= 3$$ and $$y=2.5$$
  • $$x= 2.5$$ and $$y=1$$
Solve the following pair of linear (simultaneous) equations by the method of elimination:
$$x+8y= 19 $$, $$2x+11y= 28$$
  • $$x= 3$$ and $$y= 2$$
  • $$x= 12$$ and $$y=5$$
  • $$x= 1$$ and $$y=6$$
  • $$x= 9$$ and $$y=-6$$
Solve the following pair of linear (simultaneous) equations by the method of elimination:
$$2x+7y= 39$$
$$3x+5y= 31$$
  • $$x= 1,y= 6$$
  • $$x= 7,y= 4$$
  • $$x= 2,y= 5$$
  • $$x= 3,y= 1$$
Solve the following pair of linear (simultaneous) equations by the method of elimination:
$$2x-3y= 7$$
$$5x+y= 9$$
  • $$x= 4$$ and $$y=1$$
  • $$x= 1$$ and $$y=-2$$
  • $$x= 2$$ and $$y=-1$$
  • $$x= 5$$ and $$y=-4$$
Solve the following pair of linear (simultaneous) equations by the method of elimination:
$$8x+5y= 9$$
$$3x+2y= 4$$
  • $$x= 1$$ and $$y=-2$$
  • $$x= 1$$ and $$y=-5$$
  • $$x= 3$$ and $$y=6$$
  • $$x= -2$$ and $$y=5$$
Solve the following pair of linear (simultaneous) equations by the method of elimination :
$$x+y= 7$$
$$5x+12y= 7$$
  • $$x= 11$$ and $$y=-4$$
  • $$x= 1$$ and $$y=7$$
  • $$x= 13$$ and $$y=6$$
  • $$x= 1$$ and $$y=-3$$
Solve the following pair of linear (simultaneous) equations by the method of elimination:
$$6x= 7y+7$$
$$7y-x= 8$$
  • $$\displaystyle x= 3,\displaystyle y= \displaystyle \frac{11}{7}$$
  • $$\displaystyle x= 2,\displaystyle y= \displaystyle \frac{1}{2}$$
  • $$\displaystyle x= 6,\displaystyle y= \displaystyle \frac{13}{5}$$
  • $$\displaystyle x= 4,\displaystyle y= \displaystyle \frac{-1}{2}$$
Solve the following pair of linear (simultaneous) equations by the method of elimination :
$$1.5x+0.1y= 6.2$$
$$3x-0.4y= 11.2$$
  • $$x= 4,y= 2$$
  • $$x= 2,y= 5$$
  • $$x= 3,y= 7$$
  • $$x= 1,y= 6$$
Solve the following pair of linear (simultaneous) equations by the method of elimination:
$$0.2x+0.1y= 25$$
$$2\left ( x-2 \right )-1.6y= 116$$
  • $$\displaystyle x= 50,\displaystyle y= -75$$
  • $$\displaystyle x=-29,\displaystyle y= 66$$
  • $$\displaystyle x= 100,\displaystyle y= 50$$
  • $$\displaystyle x= 60,\displaystyle y= 30$$
Solve the following pair of equations:
$$7x+6y= 71$$
$$5x-8y= -23$$
  • $$x= -5;y= 4$$
  • $$x= 3,y= -2$$
  • $$x= 5,y= 6$$
  • $$x= 1,y= 3$$
Solve the following pair of equations using substitution method:
$$\displaystyle \frac{5y}{2}-\displaystyle \frac{x}{3}= 8$$
$$\displaystyle \frac{y}{2}+\displaystyle \frac{5x}{3}= 12$$
  • $$x= 2;y= 7$$
  • $$x= 6;y= 4$$
  • $$x= 7;y= 1$$
  • $$x= 8;y= 3$$
Solve the following equations by substitution method.
$$2x+y=-2;\, \, 3x-y=7$$
  • $$x = 1, y= -4$$
  • $$x = 1, y= -1$$
  • $$x = 1, y= -3$$
  • $$x = 1, y= -5$$
Solve the following pair of equations:
$$3-\left ( x-5 \right )= y+2$$, $$2\left ( x+y \right )= 4-3y$$
  • $$x= \displaystyle \frac{7}{2},y= -\displaystyle \frac{9}{5}$$
  • $$x= \displaystyle \frac{1}{6},y= -\displaystyle \frac{4}{3}$$
  • $$x= \displaystyle \frac{26}{3},y= -\displaystyle \frac{8}{3}$$
  • $$x= \displaystyle \frac{6}{5},y= -\displaystyle \frac{7}{3}$$
Solve the following pair of equations:
$$\displaystyle \frac{1}{5}\left ( x-2 \right )=\displaystyle \frac{1}{4}\left ( 1-y \right )$$, $$26x+3y+4= 0$$
  • $$x= \displaystyle -\frac{1}{2};y= 3$$
  • $$x= \displaystyle -\frac{6}{5};y= 9$$
  • $$x= \displaystyle -\frac{8}{5};y= 8$$
  • $$x= \displaystyle -\frac{2}{3};y= 7$$
The sides of an equilateral triangle are given by $$x+3y$$;  $$3x+2y-2$$ and $$4x+\displaystyle \frac{1}{2}y+1$$ respectively. Find the lengths of the sides of the triangle.
  • $$15$$ units each
  • $$17$$ units each
  • $$12$$ units each
  • $$11$$ units each
Solve the following equations by substitution method.
$$2x-3y-3=7; \, \, 4x-5y-5=10$$
  • $$x = \displaystyle \frac{-7}{2}, y= -5$$
  • $$x = \displaystyle \frac{-3}{2}, y= -5$$
  • $$x = \displaystyle \frac{-1}{2}, y= -5$$
  • $$x = \displaystyle \frac{-5}{2}, y= -5$$
Solve the following pair of equations:

$$2x-3y-3= 0$$, $$\displaystyle \frac{2x}{3}+4y+\displaystyle \frac{1}{2}= 0$$
  • $$x= \displaystyle \frac{13}{20},y= -\displaystyle \frac{7}{10}$$
  • $$x= \displaystyle \frac{17}{20},y= -\displaystyle \frac{1}{20}$$
  • $$x= \displaystyle \frac{1}{10},y= -\displaystyle \frac{7}{10}$$
  • $$x= \displaystyle \frac{21}{20},y= -\displaystyle \frac{3}{10}$$
Pooja and Ritu can do a piece of work in $$\displaystyle 17\frac{1}{7}$$ days. If one day work of Pooja is three fourth of one day work of Ritu then find in how many days each alone will do the same work.
  • Pooja in 40 days and Ritu in 30 days
  • Pooja in 60 days and Ritu in 40 days
  • Pooja in 30 days and Ritu in 10 days
  • Pooja in 45 days and Ritu in 20 days
Solve the following equations by substitution method.
$$x-2y+2=0; \, \, x+2y=10$$
  • $$x = 4, y= 3$$
  • $$x = 1, y= 3$$
  • $$x = 9, y= 3$$
  • $$x = 5, y= 3$$
Solve the following simultaneous equations by the method of equating coefficients.$$3x-4y=7;\, \, 5x+2y=3$$ .
  • $$x = 1, y= -1$$
  • $$x = 2, y= 1$$
  • $$x = 5, y= 2$$
  • $$x = 4, y= -3$$
Solve the following simultaneous equations by the method of equating coefficients.$$\displaystyle \frac{x}{3} + \frac{y}{4} = 4; \, \, \frac{x}{2} - \frac{y}{4}=1$$
  • $$x = 2, y= 8$$
  • $$x = 6, y= 8$$
  • $$x = 7, y= 8$$
  • $$x = 1, y= 8$$
Solve the following equations by substitution method:
$$5x-2y=13; \, \, 4x+3y=15$$
  • $$x=1,y=-3$$
  • $$x=3,y=1$$
  • $$x=-1,y=3$$
  • $$x=-1,y=-3$$
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